A data-driven based low-voltage power distribution network modeling method and visualization method thereof

Abstract

The application is a kind of low-voltage power distribution network modeling and visualization method based on data driving, belongs to the technical field of smart distribution network, aiming at the problem of insufficient identification accuracy of existing research based on end measurement data to deduce low-voltage power distribution network parameters and topology structure, the application provides a kind of low-voltage power distribution network modeling and visualization method based on data driving, including collecting information based on advanced measurement system in low-voltage power distribution network, introducing user node dimension homogeneous vector, establishing the mapping relationship between it and distribution network information;Based on the mapping relationship, the perception is realized by establishing the low-voltage power distribution network physical topology-impedance data model;Based on the low-voltage power distribution network physical topology-impedance data model, a database is established and the corresponding node information is stored. The user node dimension homogeneous vector as the model input can eliminate the influence of data missing, overcome the problems of the prior art, and unify the vector dimension and data format model adaptability.

Description

Technical Field

[0001] This invention belongs to the field of smart distribution network technology, and specifically relates to a data-driven method for modeling and visualizing low-voltage distribution network. Background Technology

[0002] Accurate power grid model parameters are fundamental to power grid security analysis. Currently, transmission network parameters are mostly obtained through field measurements and verified using identification methods, effectively supporting the safety of power grid operation and the reliability of power supply. Distribution networks, however, experience rapid topological changes, have a large number of devices, and undergo frequent line maintenance and upgrades due to various reasons. Furthermore, the number of real-time monitoring devices for distribution networks is far fewer than that for transmission networks. Therefore, effectively identifying the parameters of distribution network branches has both theoretical and practical significance.

[0003] Distribution networks can be classified into high-voltage, medium-voltage, and low-voltage distribution networks according to voltage levels. Compared to medium- and high-voltage distribution networks, low-voltage distribution networks are larger in scale, more complex in structure, prone to data loss, and frequently experience user expansion and modification. This results in unclear topological relationships between distribution transformers, lines, and users, making it difficult to manually sort out these relationships. Therefore, it is urgent to study the parameters and topology identification technology of low-voltage distribution networks to improve the level of refined power grid management.

[0004] The widespread adoption of advanced metering infrastructure (AMI) has made data-driven identification of low-voltage distribution network parameters and topology possible. Even when the network structure is unknown, the network topology can be reconstructed using multi-period measurement data. However, in low-voltage distribution networks, only end-users and distribution transformers are often equipped with smart meters. For zero-injection nodes in the network, there are no measurement units available, making it impossible to directly obtain the parameters and topology of the low-voltage distribution network from the measurement information of all nodes. Existing research on deriving low-voltage distribution network parameters and topology based on end-user measurement data faces challenges in data acquisition and... During transmission, data loss can occur due to factors such as inconsistent smart meter models, unstable local channels, or human error. Random loss of user data is also a frequent occurrence, affecting the accuracy of algorithms driven by massive amounts of data. This results in inaccurate calculations of the low-voltage distribution network structure and parameters, and the identification accuracy still needs improvement. Furthermore, the process is complex, time-consuming, and inefficient. Therefore, how to provide real-time decisions based on measurements uploaded by terminal smart devices to identify low-voltage distribution network parameters and topology has become a major concern for many power industry workers and electrical engineers in recent years. Summary of the Invention

[0005] To address the shortcomings of existing research methods that derive low-voltage distribution network parameters and topology based on end-point measurement data, which suffer from insufficient accuracy, complexity, time consumption, and low efficiency, this invention provides a data-driven method for modeling and visualizing low-voltage distribution network. By utilizing measurement data with limited information, a corresponding physical topology-impedance data model of the low-voltage distribution network is trained, thereby overcoming the problems of existing technologies.

[0006] The technical solution adopted in this invention is as follows: A data-driven method for modeling and visualizing low-voltage distribution network, comprising:

[0007] S1, based on the information collected by the advanced measurement system in the low-voltage distribution network, introduces a user node dimension homogeneous vector with constant degrees of freedom, and establishes its mapping relationship with the distribution network information;

[0008] S2, based on the homogeneous vector of user node dimensions established in step 1 and its mapping relationship with distribution network information, a physical topology-impedance data model of low-voltage distribution network is established to realize the perception of the overall network structure and impedance composition of low-voltage distribution network.

[0009] S3. Based on the low-voltage distribution network physical topology-impedance data model established in step 2, a database is established and the corresponding node information is stored. The Node.js framework is used to implement the adaptive input and visualization of the model, thereby realizing the online estimation and monitoring of low-voltage distribution network parameters.

[0010] This application introduces a homogeneous vector for user node dimensions, which can determine a uniform time sampling interval granularity by setting a fixed sampling time point, while maintaining a uniform dimension. Using the homogeneous vector for user node dimensions as the input of the model can effectively eliminate the impact of missing data, overcome the problems of asynchronous time information in the distribution network and the inability of measurement devices to provide synchronized data due to communication issues, and unify the vector dimension and data format of the input data, so that the model has broad adaptability and can be applied to network sensing of various types of low-voltage distribution networks.

[0011] Furthermore, step S1 specifically involves introducing a homogeneous dimension vector X for the i-th user node at the t-th real-time measurement time point, where the degrees of freedom are constant. ui =[X ui1 ,X ui2 ,...,X uit ,...,X uiT ]; where X is the expression of the homogeneous vector of user node dimensions, u represents the data type, which includes power grid-related measurement information types, such as voltage, current, and power; t represents the real-time measurement time point, T represents the total number of sampling time points, and t takes the value range of [1,T]; i is the user node, n is the total number of user nodes, and i takes the value range of [1,n].

[0012] Further, step S2 involves the following specific operations:

[0013] S2.1, based on the Kendall correlation coefficient between homogeneous vectors of user nodes with constant degrees of freedom, find the coupling characteristics between nodes, and preliminarily identify the corresponding node connection relationships through the maximum spanning tree algorithm;

[0014] S2.2, Based on the initially identified node connection relationships, establish two typical low-voltage distribution network models and set up corresponding upstream-downstream node backtracking models for distribution network lines. Extract the features of the homogeneous vector of the coupled user node dimension through the logistic regression algorithm, and complete the classification of distribution network types.

[0015] S2.3 Based on the distribution network type and the determined upstream-downstream node backtracking model type, spectral clustering is used to identify the upstream-downstream node backtracking model, and impedance identification of the low-voltage distribution network is achieved based on voltage linear regression characteristics.

[0016] S2.4, based on the topology-impedance data of the low-voltage distribution network and the backtracking status of upstream and downstream nodes, realizes online estimation of power flow at branch nodes and segmented calculation of graded line losses.

[0017] In power distribution networks, voltage fluctuates frequently due to the uncertainty of loads at various points. Loads with relatively short electrical distances exhibit similar voltage fluctuation curves (high correlation), while loads with relatively long electrical distances show lower similarity (low correlation). By comparing the correlation coefficients between the voltage curves of smart meters of power users at different nodes, this paper examines whether a topological connection exists between two users. Therefore, this paper selects Kendall's correlation coefficient and, through classification techniques based on similarity metrics in data mining, can effectively solve the problem of verifying topological connections between users in power distribution networks.

[0018] Further, in step S2.1, let X be the homogeneous voltage vector of the user node dimension of the i-th user node and the j-th user node. Vi and X Vj There are two groups of samples, namely (X) Vi1 ,X Vj1 ), (X Vi2 ,X Vj2 ), (X Vi1 -X Vi2 (X) Vj1 -X Vj2 If the correlation coefficient is greater than 0, then the two samples are said to be consistent, and the Kendall correlation coefficient is established based on this.

[0019]

[0020] In the formula, τ is the Kendall correlation coefficient, and P is the probability density function. and These are the user node dimension voltage homogeneity vectors X Vi and X Vj The average of ; j is the user node, with a value range of [1, n];

[0021] The Kruskal algorithm is used to find the spanning tree with the highest node correlation. First, all connection weights are sorted in descending order. Then, the two nodes corresponding to the largest connection weight are added to the initial minimum spanning tree network. Then, the nodes corresponding to the largest connection weights are added to the constructed spanning tree until all n nodes are added to the sub-network, thus initially identifying the corresponding node connection relationships.

[0022] Furthermore, in step S2.2, the trunk topology of a typical overhead low-voltage distribution network "transformer-pole-user" and the tree topology of a typical cable low-voltage distribution network "transformer-branch-meter box-user" are trained on massive distribution network data using a logistic regression algorithm to achieve classification.

[0023] The low-voltage distribution network classification model expression g(x) is:

[0024]

[0025] In the formula, θ i and β i X represents the homogeneous voltage vector X of the user node dimension. Vi The power homogeneity vector X of the user node dimension Pi The corresponding parameters; γ is the error parameter;

[0026] The maximum likelihood function L(θ) of the classification model is shown in the following equation:

[0027]

[0028] In the formula, L(θ) is the maximum likelihood function of the classification model, and y is a 0-1 state variable;

[0029] In the maximum likelihood function L(θ) of the classification model, y∈{0,1}. When 0≤g(x)≤0.5, y=0, and the corresponding typical distribution network type is urban low-voltage distribution network; when 0.5<g(x)≤1, y=1, and the corresponding typical distribution network type is rural low-voltage distribution network.

[0030] Low-voltage distribution networks possess characteristics distinct from medium- and high-voltage distribution networks. Many typical low-voltage distribution networks lack internal measurement units. Furthermore, their topology differs from the main grid and medium- and high-voltage distribution networks, and smart meters primarily serve the purpose of energy metering, resulting in a limited range of measurable data types and low frequency of measurement. Therefore, classifying and modeling typical low-voltage distribution networks allows for impedance backtracking identification for different types of low-voltage distribution networks.

[0031] Furthermore, step S2.3 specifically involves the following steps:

[0032] Define w ij w represents the weight between user node i and user node j. ji That is, the weight between user node j and user node i, for an undirected topology w. ij =w ji Let d be the degree of the network node in the region. i Let the kernel function be Gaussian, then:

[0033]

[0034] In the formula, X ui and X uj Let X be the homogeneous vectors of user node dimensions for user node i and user node j, respectively, and let σ be the dimension of X. ui and X uj Standard deviation;

[0035] The degree matrix D is constructed as follows:

[0036]

[0037] The degree matrix D is an n×n diagonal matrix, and the degree d of the nodes is... i The diagonal elements that make up an n×n degree matrix D;

[0038] According to w ij Construct the weight matrix W:

[0039]

[0040] Let the Laplace matrix L = D - W, then the normalized Laplace matrix is ​​D. -1 / 2 LD -1 / 2 ;

[0041] Use G b (b=1,2,...) represents the total set of downstream nodes in the backtracking of the b-th layer of two typical low-voltage distribution networks. Let A be the mutually independent subgraphs. cut , For A cut The corresponding complement, where d cut For subgraph A cut The degree of an internal node. for With A cut The weight matrix between them, and the subgraph NCut(Acut) partitioned according to the Ncut optimal slicing method, are represented as follows:

[0042]

[0043] Let the total number of end users be k1, calculate the standard Laplace matrix D. -1 / 2 LD -1 / 2 The eigenvectors f corresponding to the k1 smallest eigenvalues ​​are normalized to form an n×k1 dimensional eigenma matrix F; let F T If F = I, then the final optimization objective is:

[0044] arg min tr(F T D -1 / 2 LD -1 / 2 F)

[0045] In the formula: I is the identity matrix of the corresponding dimension;

[0046] Clustering is performed on each row of the feature matrix F using the K-means algorithm, resulting in the downstream node set C(c1, c2, ..., c) after the node partitioning at layer b. l ...c k2 ), k2 is the total number of upstream nodes in the (b-1)th layer, c l Let l be the set of downstream nodes belonging to the same upstream node in the b-th layer, and l takes values ​​in the range [1, k2].

[0047] Based on the downstream node set and the identified upstream node set, an upstream-downstream node backtracking model is established;

[0048] Considering the phasor relationship of line voltage drop, and based on the characteristics of relatively small X / R (ratio of reactance to resistance) and reactive power at nodes in low-voltage power supply lines, the difference in voltage phase angle is ignored when modeling the equivalent circuit between upstream and downstream nodes. The voltage drop formula is approximated as follows:

[0049]

[0050] In the formula, X Vm，t X Vmi，t They are the upstream node m and the downstream node m, respectively. i (i = 1, 2, ..., n) voltage amplitude at real-time measurement time point t; X Pmi，t and X Qmi，t The downstream node m are respectively i Active power and reactive power; R i and X i They are respectively downstream nodes m i These are the resistance and reactance values ​​of the line at the terminal node; The inflow to downstream node m are respectively i The active and reactive currents; the value of m is determined based on the total number of upstream nodes;

[0051] By calculating the voltage drop at the beginning and end of the circuit, a multiple linear regression equation is established:

[0052]

[0053] Downstream node m i The active current formula for (i = 1, 2, ..., n) is:

[0054]

[0055] Downstream node m i The reactive current formula for (i = 1, 2, ..., n) is:

[0056]

[0057] The R to be estimated in the parallel circuit i X i It can be viewed as the regression coefficient of the regression equation; by substituting the sampled values ​​at different times in the time series into the multiple linear regression equation, an overdetermined system of equations is formed.

[0058] From downstream node m i The average and variance of the upstream node m voltage at real-time measurement time point t, obtained from (i = 1, 2, ..., n) as the starting point of the derivation, are as follows:

[0059]

[0060]

[0061] In the formula: (X Vm，t ) are For downstream node m i (i = 1, 2, ..., n) represents the average voltage value of upstream node m at real-time measurement time point t obtained from the derivation starting point; (X Vm，t ) var For downstream node m i (i = 1, 2, ..., n) represents the variance of the voltage value of the upstream node m at the real-time measurement time point t obtained from the derivation starting point;

[0062] Therefore, determining the resistance and reactance of each branch can be transformed into an optimization problem of finding the minimum objective function over the entire time series. Under the constraint that both resistance and reactance values ​​are greater than zero, the objective function Z(x) is established as follows:

[0063]

[0064] The impedance of the parallel line is calculated by estimating using the least squares method, and by constructing a regression equation based on the measurement data of the parallel nodes at the end of the line when the electrical quantities at the beginning of the line are unknown.

[0065] After calculating the impedance of the parallel circuit, the voltage value of the upstream node is further calculated using the multiple linear regression equation:

[0066]

[0067] Where ε represents the total error of all parallel circuits.

[0068] The low-voltage distribution network end users are clustered using a spectral clustering algorithm. Combined with the typical distribution network type to which the network topology belongs, the unique correspondence between each user and its upstream node is determined. In a typical overhead low-voltage distribution network, the upstream node obtained from the first spectral clustering is the pole, and a single clustering operation yields the "transformer-pole-user" topology. In a typical cable low-voltage distribution network, the upstream node obtained from the first spectral clustering is the meter box. A second spectral clustering operation is needed to obtain a set of branch nodes, ultimately resulting in a tree-like topology of "transformer-branch-meter box-user".

[0069] Furthermore, in step S2.4, the impedance value and node voltage value are obtained through S2.3, and the downstream node m is first derived. i (i = 1, 2, ..., n) represents the branch power loss at the terminal node:

[0070]

[0071] In the formula, For the real-time measurement time point t, downstream node m i R represents the branch power loss at the end node. i and X i These are the resistance and reactance values ​​of this section of the line, respectively. Imi，t The current flowing into node mi on this line segment is measured in real time at time point t; h is an imaginary number.

[0072] Based on the voltage, current, and power values ​​of the upstream nodes, the power distribution can be calculated:

[0073]

[0074] In the formula, X Sm，t To measure in real time the power flowing into the upstream node m at time point t, For the downstream node m at the real-time measurement time point t i Inflowing power, X Pm，t X Qm，t X represents the active power and reactive power of the upstream node m at the real-time measurement time point t, respectively. Im，t To measure in real time the current flowing into upstream node m at time point t;

[0075] For each branch, the above power flow calculation process must be performed to obtain the line power distribution of the entire topology for the next step of calculation.

[0076] In summary, the formula for the injected power at upstream node m is:

[0077]

[0078]

[0079] In the formula: X Pm，t X Qm，t These represent the injected active power and reactive power of the upstream node m in the backtracking of layer b, respectively. This represents the sum of the active power of the downstream nodes in the b-th layer backtracking. This is the sum of the reactive power of the downstream nodes in the b-th layer backtracking; For all downstream nodes m in the b-th level backtracking i This refers to the active power loss of the line at the terminal node. X represents the reactive power loss of all lines with downstream nodes as the final nodes in the b-th level backtracking; Pnext，t Let X be the active power flowing into the upstream node during the (b-1)th layer backtracking. Qnext，t This represents the reactive power flowing into the upstream node during the (b-1)th layer backtracking;

[0080] After the backtracking model of all upstream and downstream nodes in layer b and layer b-1 is completed, layer b-1 should be used as the new downstream node layer to backtrack to layer b-2, and so on, layer by layer, until the entire topology is traversed.

[0081] Furthermore, the specific process of step 3 is as follows:

[0082] S3.1, Establish a database based on the node variables in the model, create a corresponding table structure for the dimension homogeneity vector of each user node in the database, realize data interaction, and improve the corresponding interface;

[0083] S3.2, Based on the homogeneous vector of user node dimensions, establish its mapping relationship with distribution network information; input the user node measurement information that uniquely corresponds to each user node's homogeneous vector of dimensions, traverse the timestamps of the input low-voltage distribution network user measurement information, determine the real-time measurement time point t corresponding to each value and input it into the homogeneous vector of user node dimensions, as the input of the low-voltage distribution network physical topology-impedance data model, so that the low-voltage distribution network physical topology-impedance data model can be calculated, and the model result is returned after iterative verification;

[0084] S3.3, based on the model iteration verification results, updates the information of the physical topology-impedance data model in the database, establishes corresponding table structures for newly added node sets and branch sets, obtains the returned results, and uses the Node.js framework to implement the display of the visualization front-end system platform. Finally, it realizes the development of a low-voltage distribution network topology identification algorithm and power flow partitioning backtracking impedance estimation technology based on distribution transformer terminal and smart meter data mining methods, and realizes monitoring and hierarchical line loss segment calculation.

[0085] The front-end system platform, developed using the Node.js framework, interacts with the database via asynchronous AJAX requests. Simultaneously, the model algorithm recalculates after detecting data changes through the database, enabling the platform to promptly retrieve and visualize results after inputting measurement datasets. The front-end system platform comprises five modules: a dynamic input module, a network topology module, a graded line loss module, a branch power flow online estimation module, and a total network impedance module, each corresponding to the dynamic visualization of various parameters in the physical topology-impedance model.

[0086] The beneficial effects of this invention are as follows: The data-driven low-voltage distribution network modeling and visualization method of this application introduces a homogeneous vector of user node dimensions, which can determine a uniform time sampling interval granularity by setting a fixed sampling time point, and the dimensions remain uniform. Using the homogeneous vector of user node dimensions as the input of the model can effectively eliminate the impact of missing data, solve the problems of time asynchrony of distribution network information and the inability of measurement devices to provide synchronized data due to communication problems, and ensure that the low-voltage distribution network physical topology-impedance data model can unify the vector dimension and data format of the input data, so that the model has wide adaptability and can be applied to network sensing of any type of low-voltage distribution network. Attached Figure Description

[0087] Figure 1 This is a flowchart of the application;

[0088] Figure 2 This is a schematic diagram of a typical cable distribution network topology.

[0089] Figure 3 This is a schematic diagram of the topology of a typical overhead power distribution network.

[0090] Figure 4 This is a schematic diagram of a typical overhead low-voltage distribution network upstream-downstream node retrospective model;

[0091] Figure 5 This is a schematic diagram of a typical cable-based low-voltage distribution network upstream-downstream node backtracking model;

[0092] Figure 6 A schematic diagram of the voltage vectors at the beginning and end nodes of a branch; Detailed Implementation

[0093] The technical solutions of the embodiments of the present invention will be explained and described below with reference to the accompanying drawings. However, the following embodiments are only preferred embodiments of the present invention and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments in the implementation methods without creative effort are all within the protection scope of the present invention.

[0094] In this embodiment, a low-voltage distribution network front-end system platform is built based on the Node.js framework and the JavaScript front-end development language under the ES6 standard. A PHP runtime environment and MariaDB are set up on an Ubuntu server and the platform is deployed. The front-end system platform has five functional modules: dynamic input module, network topology module, hierarchical line loss module, branch power flow online estimation module, and overall network impedance module. It can also realize data interaction between the platform and the database through asynchronous AJAX requests.

[0095] A data-driven method for modeling and visualizing low-voltage distribution network, such as... Figure 1 As shown, it includes:

[0096] S1, based on the intelligent acquisition of information by the advanced measurement system in low-voltage distribution network, introduces a user node dimension homogeneous vector with constant degrees of freedom and establishes its mapping relationship with distribution network information;

[0097] Introducing a homogeneous dimension vector X for the i-th user node at the t-th real-time measurement point with constant degrees of freedom. ui =[X ui1 ,X ui2 ,...,X uit ,...,X uiT [; where X is the expression for the homogeneous vector of user node dimensions, u represents the data type, which includes power grid-related measurement information types, such as voltage, current, and power; t represents the measurement time point, T represents the total number of sampling time points, and t ranges from [1, T]; i is the user node, and its value ranges from [1, n]. In this embodiment, T is 96, that is, if data is collected at 15-minute intervals throughout the day, there are a total of 96 sampling time points.

[0098] S2, based on the homogeneous vector of user node dimensions established in step 1 and its mapping relationship with distribution network information, a physical topology-impedance data model of low-voltage distribution network is established to realize the perception of the overall network structure and impedance composition of low-voltage distribution network.

[0099] S2.1, based on the Kendall correlation coefficient between homogeneous vectors of user nodes with constant degrees of freedom, find the coupling characteristics between nodes, and preliminarily identify the corresponding node connection relationships through the maximum spanning tree algorithm;

[0100] Let X be the voltage homogeneous vectors of the i-th and j-th user nodes. Vi and X Vj There are two groups of samples, namely (X) Vi1 ,X Vj1 ), (X Vi2 ,X Vj2 ), (X Vi1 -X Vi2 (X) Vj1 -X Vj2 If the correlation coefficient is greater than 0, then the two samples are said to be consistent, and the Kendall correlation coefficient is established based on this.

[0101]

[0102] In the formula, τ is the Kendall correlation coefficient, and P is the probability density function. and These are the user node dimension voltage homogeneity vectors X Vi and X Vj The average;

[0103] The Kruskal algorithm is used to find the spanning tree with the highest node correlation. First, all connection weights are sorted in descending order. Then, the two nodes corresponding to the largest connection weight are added to the initial minimum spanning tree network. Then, the nodes corresponding to the largest connection weights are added to the constructed spanning tree until all n nodes are added to the sub-network, thus initially identifying the corresponding node connection relationships.

[0104] S2.2, Based on the initially identified node connection relationships, establish two typical low-voltage distribution network models and set up corresponding upstream-downstream node backtracking models for distribution network lines. Extract the features of the homogeneous vector of the coupled user node dimension through the logistic regression algorithm, and complete the classification of distribution network types.

[0105] The trunk topology of a typical rural low-voltage distribution network ("transformer-pole-user") and the tree topology of a typical urban low-voltage distribution network ("transformer-branch-meter box-user") are used to train models on massive distribution network data using logistic regression algorithm and achieve classification function.

[0106] The low-voltage distribution network classification model expression g(x) is:

[0107]

[0108] In the formula, θ i and β i X represents the homogeneous voltage vector X of the user node dimension. Vi The power homogeneity vector X of the user node dimension PiThe corresponding parameters; γ is the error parameter;

[0109] The maximum likelihood function L(θ) of the classification model is shown in the following equation:

[0110]

[0111] In the formula, L(θ) is the maximum likelihood function of the classification model, and y is a 0-1 state variable;

[0112] In the maximum likelihood function L(θ) of the classification model, y∈{0,1}. When 0≤g(x)≤0.5, y=0, and the corresponding typical distribution network type is urban low-voltage distribution network; when 0.5<g(x)≤1, y=1, and the corresponding typical distribution network type is rural low-voltage distribution network.

[0113] Low-voltage distribution networks possess characteristics distinct from medium- and high-voltage distribution networks. Many typical low-voltage distribution networks lack internal measurement units. Furthermore, their topology differs from the main grid and medium- and high-voltage distribution networks, and smart meters primarily serve the purpose of energy metering, resulting in a limited range of measurable data types and low frequency of measurement. Therefore, classifying and modeling typical low-voltage distribution networks allows for impedance backtracking identification for different types of low-voltage distribution networks.

[0114] S2.3 Based on the distribution network type and the determined upstream and downstream node backtracking model type, spectral clustering is used to identify the upstream and downstream node backtracking model, and impedance identification of the low-voltage distribution network is achieved based on voltage linear regression characteristics.

[0115] Define w ij Let w be the weight between user node i and user node j, for an undirected topology w. ij =w ji Let d be the degree of the network node in the region. i Let the kernel function be Gaussian, then:

[0116]

[0117] In the formula, X ui and X uj Let X be the homogeneous vectors of user node dimensions for user node i and user node j, respectively, and let σ be the dimension of X. ui and X uj Standard deviation;

[0118] Construct the degree matrix D:

[0119]

[0120] The degree matrix D is an n×n diagonal matrix, with values ​​d on the main diagonal. i The degree of the i-th point in the i-th row;

[0121] According to w ijConstruct the weight matrix W:

[0122]

[0123] Let the Laplace matrix L = D - W, then the normalized Laplace matrix is ​​D. -1 / 2 LD -1 / 2 ;

[0124] Use G b (b=1,2,...) represents the total set of downstream nodes in the backtracking of the b-th layer of two typical low-voltage distribution networks. Let A be the mutually independent subgraphs. cut , For A cut The corresponding complement, where d cut For subgraph A cut The degree of an internal node. for With A cut The weight matrix between them, and the subgraphs partitioned according to the Ncut optimal slicing method, are represented as follows:

[0125]

[0126] Let the total number of end users be k1, calculate the standard Laplace matrix D. -1 / 2 LD -1 / 2 The eigenvectors f corresponding to the k1 smallest eigenvalues ​​are normalized to form an n×k1 dimensional eigenma matrix F; let F T If F = I, then the final optimization objective is:

[0127] arg min tr(F T D -1 / 2 LD -1 / 2 F)

[0128] In the formula: I represents the identity matrix of the corresponding dimension;

[0129] Clustering is performed on each row of the feature matrix F using the K-means algorithm, resulting in the downstream node set C(c1, c2, ..., cb) after the nodes in the b-th layer are partitioned. l ...c k2 ), k2 is the total number of upstream nodes in the (b-1)th layer, c l Let l be the set of downstream nodes belonging to the same upstream node in the b-th layer, and l takes values ​​in the range [1, k2].

[0130] Based on the downstream node set and the identified upstream node set, an upstream-downstream node backtracking model is established;

[0131] Line voltage drop vector diagram as shown Figure 6As shown, based on the characteristics of low-voltage power supply lines where X / R (the ratio of reactance to resistance) and reactive power at nodes are relatively small, the voltage phase angle difference is ignored when modeling the equivalent circuit between upstream and downstream nodes. The voltage drop formula is approximated as follows:

[0132]

[0133] In the formula, X Vm，t X Vmi，t They are the upstream node m and the downstream node m, respectively. i The voltage amplitude at real-time measurement point t; X Pmi，t and X Qmi，t The downstream node m are respectively i Active power and reactive power; R i and X i They are respectively downstream nodes m i These are the resistance and reactance values ​​of the line at the terminal node; The inflow to downstream node m are respectively i The active current and reactive current;

[0134] A multiple linear regression equation was established by calculating the voltage drop at both ends of the circuit.

[0135]

[0136] Downstream node m i The active current formula for (i = 1, 2, ..., n) is:

[0137]

[0138] Downstream node m i The reactive current formula for (i = 1, 2, ..., n) is:

[0139]

[0140] The R to be estimated in the parallel circuit i X i It can be regarded as the regression coefficient of the regression equation; by substituting the sampled values ​​at different times in the time series into the equation, a multivariate linear regression equation is formed, which constitutes an overdetermined system of equations.

[0141] From downstream node m i The average and variance of the upstream node m voltage at real-time measurement time point t, obtained from (i = 1, 2, ..., n) as the starting point of the derivation, are as follows:

[0142]

[0143]

[0144] In the formula: (X Vm，t ) ave For downstream node m i (i = 1, 2, ..., n) represents the average voltage value of upstream node m at real-time measurement time point t obtained from the derivation starting point; (X Vm，t ) var For downstream node m i (i = 1, 2, ..., n) represents the variance of the voltage value of the upstream node m at the real-time measurement time point t obtained from the derivation starting point;

[0145] Therefore, determining the resistance and reactance of each branch can be transformed into an optimization problem of finding the minimum objective function over the entire time series. Under the constraint that both resistance and reactance values ​​are greater than zero, the objective function Z(x) is established as follows:

[0146]

[0147] The impedance of the parallel line is calculated by estimating using the least squares method, and by constructing a regression equation based on the measurement data of the parallel nodes at the end of the line when the electrical quantities at the beginning of the line are unknown.

[0148] After calculating the impedance of the parallel circuit, the voltage value of the upstream node is further calculated using the multiple linear regression equation:

[0149]

[0150] Where ε represents the total error of all parallel circuits.

[0151] The low-voltage distribution network end users are clustered using a spectral clustering algorithm. Combined with the typical distribution network type to which the network topology belongs, the unique correspondence between each user and its upstream node is determined. In a typical overhead low-voltage distribution network, the upstream node obtained from the first spectral clustering is the pole, and a single clustering operation yields the "transformer-pole-user" topology. In a typical cable low-voltage distribution network, the upstream node obtained from the first spectral clustering is the meter box. A second spectral clustering operation is needed to obtain a set of branch nodes, ultimately resulting in a tree-like topology of "transformer-branch-meter box-user".

[0152] S2.4, based on the topology-impedance data of the low-voltage distribution network and the backtracking status of upstream and downstream nodes, realizes online estimation of power flow at branch nodes and segmented calculation of graded line loss;

[0153] The impedance and node voltage values ​​are obtained through S2.3. First, the downstream node m is derived. i (i = 1, 2, ..., n) represents the branch power loss at the terminal node:

[0154]

[0155] In the formula, For time t, downstream node m i R represents the branch power loss at the end node. i and X i These are the resistance and reactance values ​​of this section of the line, respectively. Imi，t Let t be the current flowing into node mi on this line segment at time t; h is an imaginary number.

[0156] Based on the voltage, current, and power values ​​of the upstream nodes, the power distribution can be calculated:

[0157]

[0158] In the formula, X Sm，t To measure in real time the power flowing into the upstream node m at time point t, For the downstream node m at the real-time measurement time point t i Inflowing power, X Pm，t X Qm，t X represents the active power and reactive power of the upstream node m at the real-time measurement time point t, respectively. Im，t To measure in real time the current flowing into upstream node m at time point t;

[0159] For each branch, the above power flow calculation process must be performed to obtain the line power distribution of the entire topology for the next step of calculation.

[0160] In summary, the formula for the injected power at upstream node m is:

[0161]

[0162]

[0163] In the formula: X Pm，t X Qm，t These represent the injected active power and reactive power of the upstream node m in the backtracking of layer b, respectively. This represents the sum of the active power of the downstream nodes in the b-th layer backtracking. This is the sum of the reactive power of the downstream nodes in the b-th layer backtracking; For all downstream nodes m in the b-th level backtracking i This refers to the active power loss of the line at the terminal node. X represents the reactive power loss of all lines with downstream nodes as the final nodes in the b-th level backtracking; Pnext，t Let X be the active power flowing into the upstream node during the (b-1)th layer backtracking. Qnext，t This represents the reactive power flowing into the upstream node during the (b-1)th layer backtracking.

[0164] After the backtracking model of all upstream and downstream nodes in layer b and layer b-1 is completed, layer b-1 should be used as the new downstream node layer to backtrack to layer b-2, and so on, layer by layer, until the entire topology is traversed.

[0165] S3. Based on the low-voltage distribution network physical topology-impedance data model established in step 2, a database is established and the corresponding node information is stored. The Node.js framework is used to realize the adaptive input and visualization of the model, thereby realizing the online estimation and monitoring of low-voltage distribution network parameters.

[0166] S3.1, Establish a database based on the node variables in the model, and establish a corresponding table structure for the dimension homogeneity vector of each user node in the database so that it can interact with the dynamic input module of the platform, and improve the corresponding database, algorithm and platform interface.

[0167] S3.2, Based on the homogeneous vector of user node dimensions, establish its mapping relationship with distribution network information; input the user node measurement information that uniquely corresponds to the homogeneous vector of each user node dimension into the dynamic input module of the low-voltage distribution network online monitoring system platform, traverse the timestamps of the input low-voltage distribution network user measurement information, determine the real-time measurement time point t corresponding to each value and input it into the homogeneous vector of user node dimensions, as the input of the low-voltage distribution network physical topology-impedance data model, so that the low-voltage distribution network physical topology-impedance data model can be calculated, and the model result is returned after iterative verification;

[0168] S3.3, based on the model iteration verification results, updates the information of the physical topology-impedance data model in the database, establishes corresponding table structures for newly added node sets and branch sets, enables the platform to obtain the returned results, and uses Node.js to implement the display of the visualization front-end system platform. Finally, it realizes the development of a low-voltage distribution network topology identification algorithm and power flow partitioning backtracking impedance estimation technology based on distribution transformer terminal and smart meter data mining methods, and realizes monitoring and hierarchical line loss segment calculation.

[0169] This application introduces a homogeneous vector for user node dimensions, which can determine a uniform time sampling interval granularity by setting a fixed sampling time point, while maintaining a uniform dimension. Using the homogeneous vector for user node dimensions as the input of the model can effectively eliminate the impact of missing data, overcome the problems of asynchronous time information in the distribution network and the inability of measurement devices to provide synchronized data due to communication issues, and unify the vector dimension and data format of the input data, so that the model has broad adaptability and can be applied to network sensing of various types of low-voltage distribution networks.

[0170] In power distribution networks, voltage fluctuates frequently due to the uncertainty of loads at various points. Loads with relatively short electrical distances exhibit similar voltage fluctuation curves (high correlation), while loads with relatively long electrical distances show lower similarity (low correlation). By comparing the correlation coefficients between the voltage curves of smart meters of power users at different nodes, this paper examines whether a topological connection exists between two users. Therefore, this paper selects Kendall's correlation coefficient and, through classification techniques based on similarity metrics in data mining, can effectively solve the problem of verifying topological connections between users in power distribution networks.

[0171] Low-voltage distribution networks possess characteristics distinct from medium- and high-voltage distribution networks. Many typical low-voltage distribution networks lack internal measurement units. Furthermore, their topology differs from the main grid and medium- and high-voltage distribution networks, and smart meters primarily serve the purpose of energy metering, resulting in a limited range of measurable data types and low frequency of measurement. Therefore, classifying and modeling typical low-voltage distribution networks allows for impedance backtracking identification for different types of low-voltage distribution networks.

[0172] A typical low-voltage cable distribution network topology is usually radial, consisting of transformers, circuit breakers, disconnectors, fuses, junction boxes, meter boxes, etc., with all users located at the end of the low-voltage distribution network, such as... Figure 2 As shown, electrical energy is distributed to the distribution box via feeders or other means, and the single-phase power is sent to each meter box through different cable branches, and finally to the corresponding residents or shops; the typical overhead line low-voltage distribution network topology is a trunk line type, and electrical energy is delivered to downstream users of each phase through pole leads.

[0173] A typical overhead low-voltage distribution network topology is usually trunk-line type, with feeders laid downstream via poles, and electrical power delivered to users in each phase via lead wires. Figure 3 As shown.

[0174] The low-voltage distribution network end users are clustered using a spectral clustering algorithm. Combined with the typical distribution network type to which the network topology belongs, the unique correspondence between each user and its upstream node is determined. In a typical overhead low-voltage distribution network, the upstream node obtained from the first spectral clustering is the pole, and a single clustering operation yields the "transformer-pole-user" topology. In a typical cable low-voltage distribution network, the upstream node obtained from the first spectral clustering is the meter box. A second spectral clustering operation is needed to obtain a set of branch nodes, ultimately resulting in a tree-like topology of "transformer-branch-meter box-user".

[0175] A typical overhead power distribution network has a trunk-line topology, with electrical energy delivered to downstream users via poles and conductors. Based on this, a retrospective model of upstream and downstream nodes in a typical overhead low-voltage distribution network is established, such as... Figure 4 As shown, points m1, m2, ..., m nFor a user node, its upstream node m represents a power pole, connected to the secondary side of the distribution network via feeders, forming a "transformer-power pole-user" structure. Similarly, the typical upstream-downstream node backtracking model of a low-voltage cable distribution network is as follows: Figure 5 As shown, through user nodes m1, m2, ..., m n The process traces back to upstream node m (meter box), then back from meter box node m to branch node s, connecting to the secondary side of the distribution network via feeders, forming a "transformer-branch-meter box-user" structure. Through multiple backtracking steps, each backtracking result is used as a downstream node, and then backtracking is performed on the upstream node at the next higher level, ultimately calculating the secondary side parameter values ​​of the distribution network. Using G... b (b=1,2,...) represents the total set of downstream nodes at the b-th level of two typical low-voltage distribution networks, where each G... b In a network, downstream nodes correspond to their upstream nodes in the next higher layer, such as a set G of end users in a typical low-voltage cable distribution network. b If a set contains multiple users, then a certain table box in the upper-level table box hierarchy should be regarded as an upstream node and correspond one-to-one with the set. At the same time, this upstream node and each user in the set constitute an upstream-downstream node backtracking model.

[0176] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art should understand that the present invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments above. Any modifications that do not depart from the functional and structural principles of the present invention will be included within the scope of the claims.

Claims

1. A data-driven method for modeling and visualizing low-voltage distribution network, characterized in that, include: S1, based on the information collected by the advanced measurement system in the low-voltage distribution network, introduces a user node dimension homogeneous vector with constant degrees of freedom, and establishes its mapping relationship with the distribution network information; The specific process is as follows: Introduce the first degree of freedom with constant degrees of freedom. i The user node t Let X be a homogeneous vector of user nodes at each real-time measurement point. ui =[ X ui1 , X ui2 ,..., X uit ,..., X uiT ];in X The expression for the homogeneous vector of the user node dimension. u Representative data types include power grid-related measurement information types; t Represents the real-time measurement time point. T Represents the total number of sampling time points. t The value range is [1, ... T ]; i For user nodes, n This represents the total number of user nodes. i The value range is [1, ... n ]; S2, based on the homogeneous vector of user nodes established in step 1 and its mapping relationship with distribution network information, a physical topology-impedance data model of the low-voltage distribution network is established to realize the perception of the overall network structure and impedance composition of the low-voltage distribution network; specific operations: S2.1, based on the Kendall correlation coefficient between homogeneous vectors of user nodes with constant degrees of freedom, the coupling characteristics between nodes are found, and the corresponding node connection relationships are initially identified through the maximum spanning tree algorithm; let the th... i The user node and the first j The user node dimension voltage homogeneous vector X of each user node Vi and X Vj Each sample has two sets. The Kendall correlation coefficient is established based on the consistency between the two samples. The Kruskal algorithm is used to solve the spanning tree with the highest node correlation, so as to achieve the preliminary identification of the corresponding node connection relationship. S2.2, Based on the initially identified node connection relationships, establish two typical low-voltage distribution network models and set up corresponding upstream-downstream node backtracking models for distribution network lines. Extract the features of the homogeneous vector of the coupled user node dimension through the logistic regression algorithm, and complete the classification of distribution network types. S2.3 Based on the distribution network type and the determined upstream-downstream node backtracking model type, spectral clustering is used to identify the upstream-downstream node backtracking model, and impedance identification of the low-voltage distribution network is achieved based on voltage linear regression characteristics. In step S2.3, define w ij For user nodes i and user nodes j The weights between them, for an undirected topology w ij = w ji Let the degree of the network nodes in the region be... d i Let the kernel function be Gaussian, then: In the formula, and User nodes i and user nodes j The homogeneous vector of user node dimension, for and The standard deviation; the degree of all nodes constitutes n × n degree matrix D Diagonal elements, between nodes w ij Build n × n The weight matrix is W ; Let the Laplace matrix be set L = D - W Then the standardized Laplace matrix is ​​constructed as follows: D 1 / 2 LD 1 / 2 ; use G b , b=1,2,… This represents two typical low-voltage distribution networks. b Let the total set of downstream nodes in the layer backtracking be denoted as . A cut , for A cut The corresponding complement, according to Ncut The optimal dicing method partitions the graph to obtain corresponding subgraphs; Let the total number of end users be k 1. Calculate the standard Laplace matrix D 1 / 2 LD 1 / 2 smallest k The eigenvectors corresponding to each eigenvalue f And standardize, and finally form n × k 1-dimensional feature matrix F ; For the characteristic matrix F Each row in the dataset is clustered using the K-means algorithm to obtain the nth cluster. b The set of downstream nodes after the layer node partitioning is C ={ c 1, c 2. c l... c k2 }, k 2 is the first b -1 total number of upstream nodes, c l For the first b A layer is a set of downstream nodes belonging to the same upstream node. l The range of values ​​is [1, ... k 2]; Based on the downstream node set and the identified upstream node set, an upstream-downstream node backtracking model is established; When neglecting the difference in voltage phase angle during equivalent circuit modeling between upstream and downstream nodes, the voltage drop formula is approximated as: In the formula, , Upstream nodes m and downstream nodes m i At the real-time measurement time point t The voltage amplitude; and Downstream nodes m i Active power and reactive power; and These are the downstream nodes. m i The resistance and reactance values ​​of the line at the terminal node; , They flow into downstream nodes respectively m i The active and reactive currents; By calculating the voltage drop at the beginning and end of the circuit, a multiple linear regression equation is established; By substituting sampled values ​​from different time points in the time series into the multiple linear regression equation, an overdetermined system of equations is constructed; downstream nodes are calculated. m i , i=1,2,…,n The real-time measurement time point obtained from the starting point of the derivation. t Upstream node m The average and variance of the voltage values; The determination of the resistance and reactance of each branch can be transformed into an optimization problem of finding the minimum objective function over the entire time series. Under the constraint that the resistance and reactance values ​​are both greater than zero, the objective function Z(x) is established as follows: The least squares method is used to estimate and solve the problem, enabling the calculation of the parallel line impedance by constructing a regression equation based on the measurement data of the parallel nodes at the end of the line, even when the electrical quantities at the beginning of the line are unknown. After calculating the impedance of the parallel line, the voltage value of the upstream node is further deduced using the multiple linear regression equation. in, This corresponds to the total error of all parallel circuits; S2.4, based on the topology-impedance data of the low-voltage distribution network and the backtracking status of upstream and downstream nodes, realizes online estimation of power flow at branch nodes and segmented calculation of graded line loss; S3. Based on the low-voltage distribution network physical topology-impedance data model established in step 2, a database is established and the corresponding node information is stored. The Node.js framework is used to implement the adaptive input and visualization of the model, thereby realizing the online estimation and monitoring of low-voltage distribution network parameters.

2. The data-driven low-voltage distribution network modeling and visualization method according to claim 1, characterized in that, In step S2.2, the trunk topology of a typical overhead low-voltage distribution network "transformer-pole-user" and the tree topology of a typical cable low-voltage distribution network "transformer-branch-meter box-user" are trained on massive distribution network data using a logistic regression algorithm to achieve classification. Low-voltage distribution network classification model expression g ( x )for: In the formula, θ i and β i X represents the homogeneous voltage vector X of the user node dimension. Vi The power homogeneity vector X of the user node dimension Pi The corresponding parameters; This is the error parameter.

3. The data-driven low-voltage distribution network modeling and visualization method according to claim 1, characterized in that, In step S2.4, the impedance and node voltage values ​​are obtained through S2.3, and the downstream node is first derived. m i , i = 1,2,…,n For the branch power loss at the end node: In the formula, For real-time measurement time points t downstream nodes m i For the branch power loss at the end node, and These are the resistance and reactance values ​​of this section of the line, respectively. For real-time measurement time points t The flow of water into this section of the line mi The current value of the node; h It is the symbol for imaginary numbers; Based on the voltage, current, and power values ​​of the upstream nodes, the power distribution can be calculated: In the formula, For real-time measurement time points t upstream node m Inflow power, For real-time measurement time points t downstream nodes m i Inflow power, , These are the real-time measurement time points. t upstream node m Active power and reactive power, For real-time measurement time points t The inflow to upstream nodes m The current; For each branch, the above power flow calculation process must be performed to obtain the line power distribution of the entire topology for the next step of calculation; in summary, the upstream node is obtained. m The injection power formula is: In the formula: , The first b upstream nodes in layer backtracking m The injected active and reactive power; For the first b The sum of the active power of the downstream nodes is traced back through the layers. For the first b The sum of reactive power of downstream nodes traced back through the layers; For the first b All downstream nodes in the layer backtracking m i This refers to the active power loss of the line at the terminal node. For the first b The reactive power loss of all lines with downstream nodes as the final node in the layer backtracking; For the first b Active power flowing into upstream nodes during the -1 layer backtracking. For the first b -1 layer backtracking: reactive power flowing into upstream nodes; After the backtracking model calculations for all upstream and downstream nodes in layers b and b-1 are completed, layer b-1 should be used as the new downstream node layer to backtrack to layer b-2, and so on, progressing layer by layer until the entire topology is traversed.

4. The data-driven low-voltage distribution network modeling and visualization method according to claim 1, characterized in that, Step 3 is as follows: S3.1, Establish a database based on the node variables in the model, create a corresponding table structure for the dimension homogeneity vector of each user node in the database, realize data interaction, and improve the corresponding interface; S3.2, establish a mapping relationship between the homogeneous vector of user nodes and distribution network information; traverse the timestamps of the input low-voltage distribution network user measurement information to determine the real-time measurement time point corresponding to each value. t It also inputs the homogeneity vector of the user node dimension as input to the physical topology-impedance data model of the low-voltage distribution network, and returns the model result after iterative verification; S3.3, based on the model iteration verification results, updates the information of the physical topology-impedance data model in the database, establishes a corresponding table structure for the newly added node set and branch set, obtains the returned results, and uses the Node.js framework to implement visualization.

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